Suppose a group compiled historical data about Old Faithful Geyser (Yellowstone National Park) from 1870 to 1987. Let x, be a random variable that represents the time interval (in minutes) between Old Faithful eruptions for the years 1948 to 1952. Suppose that based on 9,320 observations, the sample mean interval was ;1 = 62.4 minutes. Let x, be a random variable that represents the time interval in minutes between Old Faithful eruptions for the years 1983 to 1987. Based on 24,755 observations, the sample mean time interval was ;2 = 73.0 minutes. Historical data suggest that o, = 8.42 minutes and , = 11.92 minutes. Let i, be the population mean of x; and let y, be the population mean of x. (a) Wwhat distribution (standard normal or Student's t) should be used to construct a confidence interval for yt; i,? Explain. O Student's t should be used because g, and g, are known. O Standard normal should be used because g, and o, are unknown O student's should be used because @, and a, are unknown. O Standard normal should be used because g, and o, are known. (b) Compute a 99% confidence interval for By~ Hy (in minutes). (Enter your answer in the form: lower limit to upper limit. Include the word "to." Round your numerical values to two decimal places.) minutes (c) Comment on the meaning of the confidence interval in the context of this problem. O There is a 0.99 probability that the previously found interval contains the difference between the population mean time between eruptions for the years 1948 to 1952 and the population mean time between eruptions for the years 1983 to 1987. O There is a 0.99 probability that the previously found interval contains the difference between the mean time between eruptions that were in the sample for the years 1948 to 1952 and the mean time between eruptions that were in the sample for the years 1983 to 1987. O with 99% confidence we can say that the previously found interval contains the difference between the population mean time between eruptions for the years 1948 to 1952 and the population mean time between eruptions for the years 1983 to 1987. O with 99% confidence we can say that the previously found interval contains the difference between the mean time between eruptions that were in the sample for the years 1948 to 1952 and the mean time between eruptions that were in the sample for the years 1983 to 1987. Does the interval consist of positive numbers only? Negative numbers only? A mix of positive and negative numbers? O The interval contains only positive numbers. O The interval contains only negative numbers. O The interval contains both positive and negative numbers